Tuesday, January 26, 2010

Grammar time, part two

Today and tomorrow, I am giving tests to each of my 70 or so students. The tests have 25 questions, 24 of which involve choosing in the form of multiple choice or true and false. The last question involves writing a sentence. Writing a sentence is exceptionally hard for Korean students.

Randomly asking a student here to make a sentence using the words "shoe" and "elephant" is to turn the classroom process on its head. To some extent, we pride ourselves on being able to make a sentence like that, but not being entirely sure what the object of a sentence is. I only learned what an object was when I started studying Korean.

As I wrote the test, I remembered Peter Mlodinow's fantastic bookThe Dunkard's Walk. Mlodinow writes that if 25 students guess randomly on a test of 10 true or false questions, there's an 75 percent chance that one will get 80%. Or, in other words, there's a 5% chance any student scoring 80% by guessing.

At first this gave the impression that over the years, a lot of dull students have walked away with good grades, but then, how many 10-question true-and-false tests did you ever write? The number of questions and the number of choices (two) help to keep the odds low. There are only 1024 possible ways to answer this test. Compare that with a trillion ways to answer a 20-question multiple-choice test with four options on each question. Mine ranks a little low, I guess, with about 2 billion possibilities.

When I first gave tests, I was dismayed by how little tests seemed to prove. If they prove anything, it wasn't what I wanted them to prove. Weak students, the sort that I thought should be punished by tests, often scored extremely well. Smart students that always work hard and should really get perfect somehow found ways to muff up questions. The result is an unsatisfying batch of tests that score somewhere in the middle.